A Smoothing Newton Algorithm for a Class of Non-monotonic Symmetric Cone Linear Complementarity Problems

作者：Lu, Nan; Huang, Zheng-Hai^*

来源：Journal of Optimization Theory and Applications, 2014, 161(2): 446-464.

DOI：10.1007/s10957-013-0436-z

• Symmetric cone complementarity problem
• Euclidean Jordan algebra
• Smoothing Newton algorithm
• Global convergence
• Local quadratic convergence

Recently, the study of symmetric cone complementarity problems has been a hot topic in the literature. Many numerical methods have been proposed for solving such a class of problems. Among them, the problems concerned are generally monotonic. In this paper, we consider symmetric cone linear complementarity problems with a class of non-monotonic transformations. A smoothing Newton algorithm is extended to solve this class of non-monotonic symmetric cone linear complementarity problems; and the algorithm is proved to be well-defined. In particular, we show that the algorithm is globally and locally quadratically convergent under mild assumptions. The preliminary numerical results are also reported.

• 出版日期2014-5
• 单位天津大学; 西安电子科技大学